Britain's biggest oil company was tonight facing an environmental disaster expected to cost more than the Exxon Valdez tanker spill as thousands of tonnes of floating oil began to reach the US Gulf coast.

As several coastal states declared a state of emergency and dispatched clean-up crews, BP was desperately trying to stem the flow of crude from its damaged offshore platform and to snuff out a growing political storm that has wiped billions of pounds off its share price.

President Barack Obama tonight sent officials from the US department of justice to monitor the company's handling of the crisis, while lawyers acting for victims of two earlier BP disasters in the US called for criminal charges and a ban on its activities there.

Fadel Gheit, an oil analyst at Oppenheimer & Co in New York, said the ultimate costs of dealing with the slick could rival that of the 1989 Exxon Valdez spill in Alaska, which led to $3.5bn in clean-up costs and $5bn in legal and financial settlements. "This is a real pickle – it's a really challenging one. It's going to be difficult to choke off this spew of oil. Any solution is going to take time and I really think the cost here is going to be in the billions of dollars," he said.

Eleven offshore workers are missing, presumed dead, after the initial explosion of the Deepwater Horizon rig last week, and BP was also severely reprimanded by safety authorities for a pipeline leak in Alaska and fatal refinery explosion.

The scale of the legal backlash facing BP was outlined by Brent Coon & Associates, an American law firm that played a large role in bringing cases against BP for the Texas City refinery fire in 2005. Today it filed a lawsuit on behalf of a rig worker injured in last week's blast, and argued that criminal charges should be brought against the company for its repeated failure to act after a series of industrial accidents in the US.

"They don't learn their lessons, they are the most arrogant bunch of bastards I've ever dealt with," said lawyer Brent Coon. "It's like they just don't care. At some point, we are going to have to put some of these executives in jail and withdraw their right to exploit our natural resources."

The chief executive of BP, Tony Hayward, said the firm, which has seen £12bn wiped off its share price since the accident, would do all it could to clean up and pay compensation. "We are taking full responsibility for the spill and we will clean it up and where people can present legitimate claims for damages we will honour them. We are going to be very, very aggressive on all of that," he said.

A BP spokesman said it was too early to say what had gone wrong or if anyone was responsible until investigations had been completed.

He pointedly referred to Transocean, the owner of the stricken rig, as having responsibility for many aspects of the drilling and declined to comment on any criminal or other legal claims.

The British oil company had outperformed its peers on the stock market last year, with a 24% increase in valuation on the back of a recovery plan implemented by Hayward. He had been forced to introduce what was thought to be much tighter controls of operations in the aftermath of accidents such as the Texas City fire – in which 15 died and 180 were injured – which led to the premature departure of his predecessor, John Browne.

Some believe BP had not been forgiven by some US politicians for lightning takeover raids in the 1990s that saw Lord Browne seize control of key US companies such as Amoco and Arco in quick succession.

But the Texas City fire gave the political establishment strong grounds for criticism after regulators damned the company for poor safety practices.

Gheit said the Deepwater spill was a "gamechanger" for BP. "It took five years for Exxon shares to shrug off the effect of the Exxon Valdez and only seabirds and otters lost their lives in that incident. With the Deepwater Horizon we are talking about eleven workers missing and after Texas City, Alaskan pipeline fractures and other incidents people are going to say there is something systematic here," he argued.Shrimp fishermen in Louisiana are also reported to have filed a class action against BP and others involved in the Gulf drilling accident, although a company spokesman said he could not confirm this.

The gathering political storm was evident when David Axelrod, a senior adviser to Barack Obama, said BP would pay for the clean-up, adding that no new oil drilling would be authorised unless proper safeguards were proven to be in place.

Tonight Alabama governor Bob Riley declared a state of emergency, saying the oil spill posed "a serious threat to our environment and economy". His declaration followed similar actions taken by the governors of Louisiana and Florida.

Meanwhile, Louisiana coastguard officials said an oil drilling rig on its way to a scrapyard had overturned in an inland waterway, but that no injuries or fuel leaks had been reported.